{
  "id": "math/0608431",
  "version": "v3",
  "published": "2006-08-16T20:55:52.000Z",
  "updated": "2007-07-04T12:52:46.000Z",
  "title": "On the Aubry-Mather theory for symbolic dynamics",
  "authors": [
    "Eduardo Garibaldi",
    "Artur O. Lopes"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We propose a new model of ergodic optimization for expansive dynamical systems: the holonomic setting. In fact, we introduce an extension of the standard model used in this theory. The formulation we consider here is quite natural if one wants a meaning for possible variations of a real trajectory under the forward shift. In another contexts (for twist maps, for instance), this property appears in a crucial way. A version of the Aubry-Mather theory for symbolic dynamics is introduced. We are mainly interested here in problems related to the properties of maximizing probabilities for the two-sided shift. Under the transitive hypothesis, we show the existence of sub-actions for Holder potentials also in the holonomic setting. We analyze then connections between calibrated sub-actions and the Mane potential. A representation formula for calibrated sub-actions is presented, which drives us naturally to a classification theorem for these sub-actions. We also investigate properties of the support of maximizing probabilities.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-07-04T12:52:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37B10"
    ],
    "keywords": [
      "symbolic dynamics",
      "aubry-mather theory",
      "maximizing probabilities",
      "calibrated sub-actions",
      "quite natural"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8431G"
    }
  }
}